MAST Math program:
AP Calculus AB
AP Calculus BC
Mulivariable Calculus/ Syracuse University
This course is designed to incorporate all of the conceptual aspects of geometry: visualization, analysis, informal reasoning, formal reasoning and deduction. This study of geometry will include components of Euclidean geometry and coordinate geometry. The primary objective of this course is to assist students with the development, verification and application of geometric concepts. Technology will be implemented into several aspects of this course, which will allow students to formulate and test geometric conjectures and patterns, and further investigate mathematical ideas.
The content of this course is organized around families of functions, including linear, quadratic, exponential, logarithmic, radical, and rational functions. As students study each family of functions, they will learn to represent them in multiple ways, such as verbal descriptions, equations, tables, and graphs. Students will also learn to model real-world situations, using functions, in order to solve problems arising from those situations. In addition, students will be introduced to the major concepts and tools for basic statistics. This course is designed to extend the students’ previous knowledge of algebraic concepts and to examine more functions. Students will continue to develop their analytical and problem solving skills, as well as enjoy an introduction to probability and statistics.
This course is designed to extend the students’ previous knowledge of algebraic concepts and trigonometric functions, to help students truly understand the fundamental concepts of algebra, trigonometry and analytic geometry, to build an intuitive foundation for calculus, and to show how algebra and trigonometry can be used to model real – life problems. A principle feature is the balance among the algebraic, numerical and verbal methods of representing problems. In addition, the students will continue to develop their analytical and problem solving skills.
After completing this course, the student should understand and have the ability to apply the basic principles of Precalculus and Calculus, should have an understanding of the process behind the development of the mathematical theories, should appreciate the importance and applications of Precalculus and Calculus concepts in his/her everyday life, should recognize the problem solving skills developed in this Precalculus and Calculus course can be applied to other courses and to real life, should be able to use technology as a tool for developing calculus skills and concepts, solving problems and modeling, should have enhanced his/her problem solving skills, and should be able to use the mathematical skills to describe and analyze physical situations and real world problems.
Initial instruction involves a comprehensive treatment of derivatives of function in one variable, and continues to the development of the definition, formulas, and applications. The next facet of the course centers on integration with applications.
The AP Statistics course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes evident in the content, skills, and assessment in the AP Statistics course: exploring data, sampling and experimentation, probability and simulation, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding. The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. Students are awarded college credit based on course proficiency.
AP Calculus AB Calculus
AB targets students who successfully complete courses in Algebra I, Algebra II, Geometry, Pre calculus and Trigonometry, and are recommended by the mathematics department. The course is divided into two main categories: differential and integral calculus. The focus of the course will be on graphical analysis of functions, and solving practical applications. Emphasis is placed on using calculus to analyze functions and their graphs, using higher level thinking skills, therefore, superior skills in algebra and trigonometry are essential for success in calculus. The course will be geared to the Advanced Placement Calculus AB Exam, which will be administered in May. Students are awarded college credit based on course proficiency.
AP Calculus BC Calculus
BC targets students who successfully complete courses in Algebra I, Algebra II, Geometry, Pre calculus, Trigonometry, and Calculus AB, and are recommended by the mathematics department. This course is divided into three main categories: differentiation, integration, and sequences and series. An intensive review of Calculus AB allows students to apply their mathematics knowledge to problems involving parametric equations, polar equations, and vectors. Superior skills in algebra and trigonometry are essential for success in Calculus BC. The course will be geared to the Advanced Placement Calculus BC Exam, which will be administered in May. Students are awarded college credit based on course proficiency.
Multivariable Calculus/Syracuse University
During this course students will be called on to demonstrate the ability to: Examine functions of several variables, define and compute limits of functions at points and define and determine continuity; Define and compute partial derivatives, directional derivatives and differentials of multivariable functions and examine conditions of differentiability; find the equation of the tangent plane to a surface at a point; Find local extreme values of functions of several variables, test for saddle points, examine the conditions for the existence of absolute extreme values, solve constraint problems using Lagrange multipliers, and solve related application problems; Use rectangular, cylindrical and spherical coordinate systems to define space curves and surfaces in Cartesian and parametric forms; Integrate functions of several variables; Examine vector fields and define and evaluate line integrals using the Fundamental Theorem of Line Integrals and Green’s Theorem; compute arc length; and Define and compute the curl and divergence of vector fields and apply Green’s Theorem, Stokes’ Theorem and the Divergence Theorem to evaluate line integrals, surface integrals and flux integrals
Students are awarded college credit based on course proficiency.